Climatic ChangeDOI 10.1007/s10584-012-0487-4

Climate policy under uncertainty:a case for solar geoengineering

Juan B. Moreno-Cruz · David W. Keith

Received: 14 December 2009 / Accepted: 13 April 2012© The Author(s) 2012. This article is published with open access at SpringerLink.com

Abstract Solar Radiation Management (SRM) has two characteristics that make ituseful for managing climate risk: it is quick and it is cheap. SRM cannot, however,perfectly offset CO2-driven climate change, and its use introduces novel climate andenvironmental risks. We introduce SRM in a simple economic model of climatechange that is designed to explore the interaction between uncertainty in theclimate’s response to CO2 and the risks of SRM in the face of carbon-cycle inertia.The fact that SRM can be implemented quickly, reducing the effects of inertia,makes it a valuable tool to manage climate risks even if it is relatively ineffectiveat compensating for CO2-driven climate change or if its costs are large comparedto traditional abatement strategies. Uncertainty about SRM is high, and decisionmakers must decide whether or not to commit to research that might reduce thisuncertainty. We find that even modest reductions in uncertainty about the side-effects of SRM can reduce the overall costs of climate change in the order of 10%.

1 Introduction

It appears to be technically feasible to engineer an increase in albedo, a planetarybrightening, as a means to offset the warming caused by carbon dioxide (CO2) andother greenhouse gases through Solar Radiation Management (SRM) (Keith andDowlatabadi 1992; Keith 2000; Crutzen 2006; Shepherd et al. 2009). However, thecooling produced by SRM does not exactly compensate for the warming caused by

J. B. Moreno-Cruz (B)School of Economics, Georgia Institute of Technology,221 Bobby Dodd Way, Atlanta, GA 30332, USAe-mail: juan.moreno-cruz@econ.gatech.edu

D. W. KeithKennedy School of Government and School of Engineering and Applied Sciences,Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

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CO2-driven climate change; and any particular method of SRM will no doubt entailother risks and side-effects (e.g. Bala et al. 2008; Ricke et al. 2010). Nevertheless,SRM may be a useful tool to mange climate risks (Wigley 2006). In this paper we askhow optimal policy is affected by risk regarding the side-effects of SRM, in the faceof uncertainty about the magnitude of the damages caused by CO2-driven climatechange.

To answer this question we construct a simple model that captures the followingstylized facts about climate change and SRM:

1. The carbon-climate system has inertia. There is a lag between the response ofthe climate system and the anthropogenic carbon emissions that cause climatechange. The inertia of the carbon-climate system makes it impossible to quicklyreduce climate risk by reducing emissions, as it is expected that 40% of the peakconcentration of CO2 will remain in the atmosphere 1000 years after the peak isreached (Solomon et al. 2009).

2. Climate change damages are uncertain. The amount of climate change resultingfrom a given emissions trajectory is uncertain, as are the resulting economic(or other) damages. Moreover, this uncertainty is irreducible over a timescaleof decades during which we will make near-term decisions about emissionsabatement (Morgan and Keith 1995; Zickfeld et al. 2010).

3. SRM is fast. A reduction in the incoming radiation has relatively instantaneouseffects on global temperature (Caldeira and Matthews 2007; Robock et al. 2008).Nature gives an example of how quickly temperature responds to changes in ra-diative forcing: after Mount Pinatubo’s explosion around 20TgS were depositedin the stratosphere, global surface temperatures cooled about 0.5◦C over thefollowing year (Soden et al. 2002).

4. SRM is inexpensive. At this stage, little is known about the technical costs ofSRM, but some preliminary studies have suggested that SRM could offset theincrease in global average temperature due to CO2 at a cost 10 to 1000 timeslower than achieving the same outcome by cutting emissions (McClellan et al.2010; Robock et al. 2009; Shepherd et al. 2009).

5. SRM cannot eliminate carbon-climate risk. SRM technologies can interveneto restore the surface temperature by reducing the incoming solar radiation.This intervention, however, cannot eliminate all the damages caused by climatechange. In particular, the temperature compensation has a different regionaldistribution, that leaves the poles under compensated while the equator is overcompensated (Caldeira and Matthews 2007). Moreover, the accumulation ofgreenhouse gases has direct implications on the precipitation patterns (Allen andIngram 2002); and, in the case of CO2, ocean acidification (Caldeira and Wickett2003, 2005).

6. SRM introduces damages. There is an increase in the risks of destruction ofstratospheric ozone due to SRM implementation (Solomon 1996, 1999). More-over, sulfuric acid deposition may create health and regional problems (Crutzen2006); although recent literature suggests these effects are small (Kravitz et al.2009). Also, recent numerical simulations show that SRM will affect precipitationpatterns and volumes, possibly causing droughts in large regions of the planet(e.g. Ricke et al. 2010).

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Our goal is to explore the trade-offs between the advantages and disadvantages ofSRM in a cost minimizing optimal-decision framework that we intend to be as simpleas possible while still capturing all of these stylized facts. The advantages of SRM tomanage climate risks are twofold. First, it is inexpensive compared to abatement, andsecond it allows rapid action avoiding some of the inertia of the carbon system. Thecorresponding disadvantages of SRM are that it imperfectly compensates for CO2

driven warming and it may introduce new environmental risks.In our model, the objective of the decision-maker is to minimize the expected

total costs of managing climate change. The costs of climate change are the sum ofthe costs of abatement and SRM activities plus any economic damages. The costsof abatement and SRM are increasing and convex functions of their arguments,while economic damages are the sum of the damages arising from greenhouse gasconcentrations—such as temperature changes and ocean acidification—and thosearising from the side-effects of SRM. The damages from temperature are a quadraticfunction of the change in global surface temperature; which, in turn, is proportionalto radiative forcing. The damages from ocean acidification arise due to the increaseof CO2 concentrations in the oceans; which, in turn, affects marine life and theeconomic activities associated with it, i.e. fishing and tourism. The damages arisingfrom the side-effects of SRM are assumed to be a quadratic function of the total levelof SRM.

As a simple way to capture climate-carbon inertia we use a two-stage decisionframework in which the abatement decisions are made in the first period and SRMdecisions are made in the second. In between periods, the decision maker learns thetrue sensitivity of the climate (Fig. 1). Because temperature depends on cumulativeemissions, we assume emissions are irreversible (Matthews et al. 2009) and in thatsense, only the level of abatement implemented before learning about the sensitivityof the climate system can help reduce damages caused by temperature changesand ocean acidification. The climate system, however, responds quickly to changesin radiative forcing in the form of SRM. This quickness of response allows SRMto reduce temperature damages after learning about the sensitivity of the climate;hence, eliminating the inertia associated with other forms of climate interventionand abatement. Damages take place in the second period, after SRM decisions aremade.

The approach in this paper has proven to be useful for the economic analysis ofclimate change and we expect it to be equally insightful for the economic analysis ofSRM [see Weitzman (2009) for a recent application of a two period model to analyzeclimate change policy, and Goulder and Mathai (2000) for an example of the useof a cost minimizing framework with increasing and convex costs to analyze climatepolicy]. Five caveats, however, are important for our analysis:

• The optimal policy assumes a centralized decision maker. In practice, manycountries will decide how to implement SRM amongst themselves. The strategicinteraction among countries may lead to under or over provision of either SRMor abatement (see Millar-Ball 2012; Moreno-Cruz 2011).

• A centralized decision maker minimizes changes in global mean temperatureand other damages at a global scale. By making this assumption, we eliminate all

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Climate Uncertainty Resolved

Uncertainty SRM

Resolved

Total Costs

Learning: SRM

Uncertainty Reduced

Abatement Decision

SRM Decision

FIRST PERIOD SECOND PERIOD

SRM as Insurance

Second Stage Learning (2L)

First Stage Learning (1L)

Climate Uncertainty Resolved

Uncertainty SRM

Resolved

Total Costs

Abatement Decision

Decision

SRM Decision

Learning: SRM

Uncertainty Reduced

Climate Uncertainty Resolved

Total Costs

Abatement Decision

SRM Decision

No Learning (NL)

Climate Uncertainty Resolved

Uncertainty SRM

Resolved

Total Costs

Abatement SRM Decision

Fig. 1 Timing of decisions and information in the two-period model. The top schematic shows thetiming when SRM is used as an insurance in Section 3. The bottom three schematics show thescenarios in Section 4. They vary depending on whether decisions are made before or after learningabout the SRM damages. Decisions are represented by rectangles, while uncertain outcomes arerepresented by circles. SRM uncertainty is represented with blue circles. Learning is represented withred circles. Payoffs are represented by hexagons. The first schematic shows the timing of decisionswhen there is no learning (NL scenario). The second schematic describes the scenario when learningtakes place before SRM decisions are made, but after abatement decisions are made (2L scenario).The third schematic describes the scenario when learning takes place before abatement and SRMdecisions are made (1L scenario)

considerations to regional inequalities that may arise from the implementationof SRM [see Moreno-Cruz et al. (2012) and Ricke et al. (2010) for a detailedtreatment of the inequalities introduced by SRM]. Nonetheless, understandingthe optimal policy is important as it serves as a benchmark with which otherpolicies may be compared.

• Use of a static two-period model limits its application in two important aspects.First, it cannot be used to analyze time dependent optimal policies where SRMis introduced incrementally. Instead we concentrate on SRM as a tool to dealwith low-probability high-consequence impacts that are colloquially referred toas “climate emergencies”. Second, the model cannot address damages due torapid temperature changes associated to the sudden interruption of an SRMprogram.

• By considering damages only in terms of reduction in economic output we areneglecting aspects of the problem that do not easily fit this framework such asnon-monetary environmental values. This assumption, of course, neglects the

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ethical issues associated with the direct manipulation of the climate implied bySRM. We believe these ethical concerns are crucial for the analysis of SRM asare the issues of uncertainty and inertia that we treat here.

The rest of the paper proceeds as follows. In Section 2 we introduce and calibratethe model. In Section 3 we introduce uncertainty on the climate system and analyzethe role of SRM in dealing with high-impact, low-probability outcomes. In Section 4,we deal with the uncertainty attached to the damages from SRM and analyze thevalue of reducing this uncertainty. We draw conclusions in Section 5.

2 A general description of the model

2.1 Temperature, abatement and SRM

When the concentration of greenhouse gases increases in the atmosphere it altersthe balance between incoming solar radiation and outgoing terrestrial radiation,resulting in an increase in the mean global temperature of Earth. Radiative forcingdescribes how the radiation balance is altered by human activity. Radiative forcing,R, is a function of the concentration of CO2 in the atmosphere, S, relative to thepreindustrial level, S0:

R = β ln(S/S0

)(1)

where, according to the IPCC (2007), β = 5.35 watts-per-meter-squared [Wm−2].Abatement, which we denote by A, refers to measures that reduce the concentrationlevel of CO2 in the atmosphere. In particular, assume that S = SBAU − A, whereSBAU is the business as usual concentration of CO2 in the atmosphere measured inparts per million [ppm].

Changes in mean global temperature, �T—measured in ◦C—are defined as alinear function of radiative forcing, R:

�T = λR (2)

where λ is the climate sensitivity parameter with units ◦C m2/W.When SRM is introduced in the model, the relation between CO2 concentrations

and temperature is altered. We measure SRM, G, in terms of its radiative forcingpotential and, since temperature change is a linear function of radiative forcing, Eq. 2can be written as:

�T(A, G) = λ

(β Ln

(SBAU − A

S0

)− G

)(3)

2.2 Economic damages

We represent total climate damages as the sum of impacts from three different sources:temperature, SRM and uncompensated CO2 damages (e.g. ocean acidification). Fol-lowing Nordhaus (2008), we assume temperature damages are quadratic. FollowingBrander et al. (2009), damages from ocean acidification are also quadratic on theconcentration of CO2. We assume that SRM damages are also a quadratic function

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of the total level of SRM.1 To be able to compare the different sources of impacts,we express damages in terms of reductions in economic output. Thus, total damagesare given by:

D(A, G) = ηS(SBAU − A)2 + ηTλ2 (�T(A, G))2 + ηGG2 (4)

where ηS(SBAU − A)2 are the damages caused by ocean acidification and otheruncompensated damages from CO2, ηTλ2 (�T(A, G))2 are damages caused bytemperature changes, and ηGG2 are the damages caused by the side-effects of SRM.In Eq. 4, when A equals SBAU and G equals zero, damages are zero. However, whenA is less that SBAU , damages are always positive, showing the inability of SRM toperfectly compensate for greenhouse gas driven climate change (see bottom panel inFig. 2). That is, although technically SRM can reduce temperature changes to zero,it may do so at the expense of other economic damages.

2.3 Implementation costs

We assume that abatement costs are increasing and convex. In particular, followingNordhaus (2008), we have:

�(A) = KA Aα (5)

where KA has units [$/ppm] and α = 2.8.Following Keith and Dowlatabadi (1992) we assume that SRM costs are linear

and given by

�(G) = KGG (6)

where KG has units [$/(Wm−2)].Total social costs are the sum of the implementation costs, given by Eqs. 5 and 6,

and the economic damages given by Eq. 4. The optimal policy consist of the level ofabatement and the level of SRM that minimize total social costs.

2.4 Calibration

We use the year 2100 as our planning horizon, a common target in the analysisof climate change policy.2 To calibrate our model, we use the projected costs anddamages in 2100 reported by the DICE-2007 model (Dynamic Integrated Model ofClimate and the Economy) (Nordhaus 2008). We complete the information neededfor our calibration using data from the IPCC (2007) and publications related tothe costs of SRM. The information given below is, unless otherwise noted, fromNordhaus (2008). The assumptions and calibrated values are summarized in Table 1.

We calibrate costs and damages as percentages of global GDP, when we reportdollar values we assume global GDP to be around $50 trillion per year (World Bank,World Development Indicators). Although not relevant for our study, incorporating

1There is not evidence of how steep the damages from SRM are. By choosing quadratic damages weare assuming they have the same weight as other climate related damages.2As suggested by the reviewers, we analyzed the results for different target years, 50 years from nowand 150 years. All the qualitative results are the same.

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, Wm

-2

Expected Valueof SRM

AbatementR

adia

tive

forc

ing

SRM,high climate impacts .

SRM,low climate impacts .

ηG

Wi h SRM

ure

Cha

nge,

0 C

t

Without SRM

Tem

pera

tu%

GD

P

Impacts of SRM, G

With SRM

Without SRM

pect

ed C

osts

, % Without

Temperature onlyDamages ( S=0)

Impacts of SRM, G

Exp

η

η

η

Impacts of SRM,

Fig. 2 Optimal climate policy. The horizontal axis is the impacts of SRM expressed as a fractionof the business-as-usual climate damages. For example, when ηG = 0.5DT , the impacts of SRM areequivalent to 50% of the damages from CO2-driven climate change. The vertical axis is in units ofradiative forcing (Wm−2). The top panel shows the optimal policy measured in terms of radiativeforcing potential (Wm−2). The middle panel presents the temperature change measured in ◦C. Thesolid line shows the results with SRM, and the dashed line shows the results without SRM. The bottompanel shows the expected costs of implementing the optimal policy as a fraction of global GDP. Theorange lines show the expected total costs with only temperature damages. The difference betweenthe solid black line and the solid orange line is the fraction of costs that cannot be compensated usingSRM

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Table 1 Calibration of model

Assumptions

Climate parameters Definitions

SBAU = 685 ppm Business as usual concentration of CO2

S0 = 270 ppm. Preindustrial concentration of CO2

RBAU = 4.98 W/m2 Business as usual radiative forcingTBAU = 4.28◦C Business as usual temperature change

Calibration

Economic parameters Notes

KA = 6.8 × 10−7 Reducing temperature change in 2100 by 1◦C from BAU[%GDP/ppm] costs 1% of global GDP and reducing temperatures by 1◦C

relative to BAU requires a CO2 reduction of 134 ppm.KG = 5.7 × 10−4 We assume the costs of SRM are 1% of the costs of abatement

[%GDP/(Wm−2)] (McClellan et al. 2010; Shepherd et al. 2009) andperformed sensitivity analysis for values between10% and 100% of the costs of abatement.

ηT = 0.32 [%GDP/◦C] If no action to deal with climate change is taken, around 3%of global GDP will be lost in 2100, orDT ≡ 0.03GDP = 1

2 ηT T2BAU

ηS = 1.3 × 10−6 Ocean acidification damages add 10% to the total impacts[%GDP/ppm] from climate change (Brander et al. 2009), or

0.1DT = 12 ηS(SBAU − S0)

2

discounting is simple. For example if we assume a discount rate of 1%, the yearlyGDP value would be equivalent to $33 trillion. If we assume a discount rate of7%, yearly GDP would be $7 trillion. Economic growth is equally easy to introduce.Introducing economic growth at a rate of 2.5% will yield a yearly GDP value of $200trillion. Considering a discount rate close to the rate of economic growth would leavethe yearly value of GDP at around $50 trillion.

There is insufficient information to allow us to quantify the risks of SRM, ηG, withany confidence, so we treat them parametrically. In Section 3 we analyze optimalpolicy as a function of ηG and in Section 4 we introduce uncertainty and learningon ηG.

3 Climate sensitivity uncertainty: SRM as insurance

In this section we analyze the role of SRM in dealing with the uncertainty sur-rounding the climate’s response to changes in the atmospheric concentration of CO2.Specifically, we made the climate sensitivity parameter, λ, random. We define therandom variable λ̃, to introduce the uncertainty of the response of the climate system.λ̃ follows a binomial distribution of the form:

λ̃ ={

λH = 2.3 with probability p = 0.1λL = 0.7 with probability 1 − p = 0.9.

(7)

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Notice that the mean of this distribution is 0.86, which is consistent with recentestimates (IPCC 2007).3 We choose this distribution of λ̃ to capture the idea oflow probability-high impact events that are characteristic of fat-tail distributionscommonly associated to climate sensitivity (Roe and Baker 2007; Weitzman 2009).This is of course a simple approximation that allows us to introduce risk in the climatesystem without increasing the complexity of the model. The qualitative results of ourpaper would remain the same if we introduce a continuous distribution with fat-tails.

As we mentioned in the introduction, to capture climate-carbon inertia, decisionsabout abatement and SRM are made sequentially. Abatement decisions are madein the first period and SRM decisions are made in the second period. In betweenperiods, the true climate sensitivity is revealed. Here SRM decisions are made underperfect information, but we will relax this assumption in Section 4 (see Fig. 1).

We introduce the imperfection of SRM parametrically; that is, the optimal level ofabatement and the optimal level of SRM are a function of the magnitude of the sideeffects of SRM, ηG. We allow damages from SRM to be higher than those induced byCO2-driven climate change, so ηG ∈ [0, 1.5DT ] where DT = $11.4 × 1012/(Wm−2).That is, when ηG = DT , reducing temperature changes to zero using only SRMmay create damages just as large as if temperature were equal to its business asusual level. By setting the upper limit at ηG = 1.5DT we try to highlight the roleof SRM as an insurance. This limit, however, can be too high. The most commonlydiscussed direct impact of SRM (using stratospheric aerosols) is ozone loss. Estimatesof the economic losses due to ozone depletion are in the order of US$1.1 trillionbetween 1987 and 2060. That is equivalent to 0.03% of global GDP, or (1/100)DT

(Environment Canada 1997; Sunstein 2007).The top panel in Fig. 2 shows the optimal policy. As expected, SRM is a decreasing

function of ηG while abatement is increasing in ηG. Thus, abatement and SRMare technical substitutes: if SRM is costly, then it is optimal to implement moreabatement. Also, the optimal level of SRM is always higher in the high-sensitivityoutcome (λ = λH) compared to the low-sensitivity outcome (λ = λL). This is theresult of the assumption that SRM can be chosen after learning about the climatesensitivity of the system. Moreover, in the case of an unlucky outcome, SRM is usedmore than abatement, even if damages from SRM are higher than DT .

The middle panel in Fig. 2 shows temperature with and without SRM. We cansee that temperature change increases when the damages from SRM increase.Temperature increases because there is a reduction in the level of SRM that is lessthan compensated by the increase in abatement levels; which results from the factthat abatement costs are increasing and convex.

The bottom panel in Fig. 2 shows the total costs of managing climate change as afunction of the marginal damages from SRM, ηG. As expected, total costs are higherwhen damages from SRM become larger. If SRM was harmless, that is ηG = 0, thesavings relative to the case of no SRM would be around 2% GDP or $1 trillion per

3The probability distribution described in Eq. 7, albeit quite simple, captures the main characteristicsof the climate distribution described by the IPCC. According to the IPCC (2007) “climate sensitivityis likely to be in a range of 2–4.5◦C with a best estimate of about 3◦C,” while “values substantiallyhigher than 4.5◦C cannot be excluded.” Using the simplified expression for radiative forcing obtainedfrom the IPCC Third Assessment Report, we find that with probability 0.9 climate sensitivity will be2.6◦C and with probability 0.1 climate sensitivity will be 8.5◦C. On average, climate sensitivity is3.2◦C.

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year, which is equivalent to a reduction in the expected costs of climate change closeto 85%. If on the other hand ηG = DT , the cost reduction due to the introduction ofSRM is around 1.1%GDP or $550 billion per year, which is equivalent to a reductionin the expected costs of climate change close to 50%. To illustrate the role that theuncompensated damages from CO2 play in the model, we set ηS = 0 (orange lines inlower panel of Fig. 2). The difference between the black and orange lines are due tocosts such as ocean acidification that cannot be compensated by SRM even if thereare no damages from SRM, (ηG = 0).

We find that it is still optimal to implement high levels of SRM even if themarginal damages from SRM are higher than those of climate change (ηG = 1.5DT).This counter-intuitive result arises because SRM can be implemented after theuncertainty about climate sensitivity is resolved. The signal advantage of SRM is itsquick response: even if damages from SRM are substantially high, it is still valuableto have SRM available, as a complement to abatement measures, in case the climatesensitivity is high. Consider the counterfactual: without SRM it is difficult to boundclimate damages in the face of climate sensitivity uncertainty and inertia as arguedby Roe and Baker (2007) and Weitzman (2009).

4 Uncertain SRM: assessing the value of learning about the side-effects

In this section we explicitly introduce uncertainty about the damages from SRM.We examine the effect that reducing this uncertainty has on the optimal policy andthe total costs of addressing climate change. Uncertainty about the risk and theeffectiveness of SRM may be reduced by researching and engaging in the smallscale implementation of SRM. We describe the reduction of uncertainty–achievedby research or otherwise—as learning.

The implications of learning for the optimal policy depends strongly on whenlearning occurs in relation to decisions. We treat three scenarios (Fig. 1). Thefirst scenario assumes no learning (NL), or equivalently that learning occurs afterabatement and SRM are chosen. In the second we assume that learning occurs beforeSRM decisions are made, but after abatement is chosen; we refer to this as secondstage learning—2L. In the third scenario, we assume that learning occurs beforeabatement and SRM decisions are made; we refer to this as first stage learning—1L.

To introduce risk associated with SRM, we treat the damages due to SRM, ηG, asa random variable η̃G that follows the distribution:

η̃G ={

ηHG = DT with probability q = 0.5ηL

G = 0 with probability 1 − q = 0.5.(8)

which has an expected value of 0.5DT . When q = 0.5, we have no informationregarding whether damages from SRM are larger or smaller than those of climatechange. In this case, and due to the linearity of the model imposed by our assumptionof quadratic damages, the optimal policy is equal to the case of no uncertaintywhen ηG = 0.5DT . This is also true for other probability distributions that preservethe mean of the original distribution. The linearity of the model with respectto the choice of SRM implies that the decision maker is risk neutral. This veryimportant characteristic allows us to concentrate on the value of learning that reducesuncertainty (Baker 2006).

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, W

m-2

Abatement

SRM,Low SRM Impacts

High SRM ImpactsSRM,

Rad

iativ

e fo

rcin

g

Expected Value of SRM

1L, First Stage Learning

2L, Second Stage Learning

Amount of learning, M

Total Costs,

Cos

ts,

%G

D Low SRM Impacts Total Costs, High SRM Impacts

Expected Costs

Exp

ecte

d

Amount of learning, M

1L, First Stage Learning

2L, Second Stage Learning

, %N

L C

osts

pect

ed S

avin

gs

1L, First Stage Learning

Amount of learning, M

Ex 2L, Second Stage Learning

Fig. 3 The effects of learning on the optimal levels of abatement and SRM, and its implicationsfor total costs, as a function of the amount of learning, M. The second stage learning (2L) scenariois denoted by dashed lines, the first stage learning (1L) scenario is denoted by solid lines, and theNo Learning scenario corresponds to M = 0. The top panel shows the effects of learning on theexpected level of SRM and abatement. The blue line shows the expected level of SRM in the casewhere learning reveals that the SRM impacts are worse than expected, while the green line showsthe converse. In red is the expected value of SRM when the probability of learning that the damagesfrom SRM are larger or smaller than the damages from climate change is 0.5. The purple lines showsthe optimal level of abatement, A. The purple dotted lines show the level of abatement in the 1Lscenario. The middle panel shows the expected costs, with the same convention as the top panel. Thebottom panel shows the total savings. Total savings are the difference between the total costs of theoptimal policy when there is no learning and the corresponding learning scenario

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We assume that learning increases the spread of the original distribution byskewing the probability towards one of the two outcomes. Learning is equally likelyto show that the damages from SRM are equal to the damages from climate change,ηG = DT , or to show they are zero, ηG = 0. That is, learning does not change theexpected value of ηG. In the case where, with probability 0.5, learning reveals thatthe impacts are more likely to be worse than expected, the distribution of η̃G takesthe form:

η̃G ={

ηHG = DT with probability qH = 0.5 + MηL

G = 0 with probability 1 − qH = 0.5 − M.(9)

where M ∈ [0, 0.5] describes the amount of learning that occurs. On the other hand,if learning reveals that low impacts from SRM are more likely, then the distributionof η̃G takes the form:

η̃G ={

ηHG = DT with probability qL = 0.5 − MηL

G = 0 with probability 1 − qL = 0.5 + M.(10)

We present our analysis as a function of M, the amount of learning that occurs.When M = 0 no learning has occurred. Whereas when M = 0.5, learning has fullyeliminated uncertainty.

Figure 3 shows the effects of learning on the optimal policy (top panel), theexpected costs of climate change (middle panel), and the net savings or expectedvalue of information (bottom panel), as functions of the amount of learning, M. Firststage learning (1L) is preferred to second stage learning (2L) for two related reasons.First, it allows better decisions in terms of SRM: SRM is lower when learning revealshigh SRM damages and SRM is higher when learning reveals low SRM damages.This tendency is accentuated when learning is larger (M → 0.5). Second, the valueof learning is an increasing function of the amount of learning and it is higher underfirst stage learning (1L).

The top panel in Fig. 3 also shows that the expected level of abatement does notchange significantly with early (1L) or late (2L) learning compared to the no learning(NL) scenario. This suggest that, at least for the optimal policy, learning about SRMdo not affect the expected value of abatement. Of course, the realized—as opposedto expected—value of abatement does strongly depend on the outcome of learning.

5 Conclusions

We explore a simple model in which a decision maker chooses the level of emissionsabatement and SRM that minimizes the costs of climate change in the face ofuncertainty about the impacts of both emissions and SRM. We draw two mainconclusions. First, imperfect SRM is an effective means to manage the uncertaintyin the climate response because it can be implemented quickly after this uncertaintyis resolved, providing a tool to manage the inertia in the carbon-climate decisionproblem. Without SRM, the existence of high-consequence low-probability climateimpacts, combined with the irreversibility of emissions, may force very high levelsof abatement and hence high costs. In our model, we find that SRM is used in thecase of an unlucky (high-impact) outcome even if the damages from SRM exceedthe expected damages from climate change. Under the same assumption about

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the damages from SRM, SRM is substantially reduced when climate impacts arerelatively low.

Second, we find that learning about SRM—that is the value of informationassociated with reducing the uncertainty about the side-effects of SRM—can reducethe overall costs of climate change in the order of 10%, depending on the amount oflearning. Suppose learning about SRM reduced the expected cost of climate changeby 5%. We can compare these savings, equivalent to 0.05% of world GDP, withthe current spending on SRM research which is less than $10 million per year, or0.00002% of GDP; though we cannot, of course, conclude that learning will beproportional to spending since we don’t know how effective this research will be inreducing uncertainty about SRM. Moreover, this specific numerical result dependson the calibration of the model and on the assumptions about the prior probabilitydistribution over the side-effects of SRM.

The model is a highly simplified representation of the problem and its applicabilityis limited by the caveats presented in the introduction to this paper. Also, the modelis afflicted by the same constraints attached to any model of climate policy thatsupposes a single decision maker; namely, no strategic interaction, no asymmetriesand therefore, no distributional issues. We have used, however, a calibration ofclimate damages and abatement that is widely used and is representative of resultsderived in many complex models. Hence, the limitations of the model likely do notaffect its main result; that is, SRM is valuable for managing climate risk, not becauseof its low cost, but because it can be implemented quickly if we discover that climateimpacts are high, a “climate emergency.”

Acknowledgements The authors want to thank four anonymous referees, Kate Ricke, DanielDutton, Sjak Smulders, Gregory Nemet and participants at WCERE 2010 for comments on an earlierversion of this paper.

Open Access This article is distributed under the terms of the Creative Commons AttributionLicense which permits any use, distribution, and reproduction in any medium, provided the originalauthor(s) and the source are credited.

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